Geographically, there are voting districts, taxing districts, and school districts. There are also subdistricts. I have found different spellings of this word (subdistrict, sub district, sub-district). Which one is correct for the USA?
COCA tells us that in its American literature corpus there are 24 instances of subdistrict versus 18 of sub-district. BNC (the British corpus) has no matches for subdistrict, but 9 for sub-district. Dictionary.com and Merriam-Webster have their entries without a hyphen (subdistrict). The OALD, significantly, does not have an entry for subdistrict.
In this case, neither is incorrect in America, though subdistrict appears to be slightly preferred. As tchrist comments below, a good American rule of thumb is that productive prefixes such as un-, non-, sub-, etc, should not take hyphens. However, in British English, subdistrict appears to be rare (if not incorrect). For further information on hyphenating, see this post:
For the most part, compound words that are created by adding a prefix are not hyphenated.
Disclaimer regarding Ngram chart: see this meta post for important info on this internet resource.